I'd like to know where I can find information about a class of objects which I think deserve to be called twisted equivariant modular forms. Let me guess a definition, indicate how it can be made more ...

I'm looking for examples of the following phenomena. Let $X$ be a reasonable space (say, a CW complex) and $G$ be a finite group acting on $X$. For all $k \geq 1$, the projection map $X \rightarrow ...

Thanks to the work of Cisinski-Deglise: http://arxiv.org/abs/0912.2110, we now have a triangulated category of `motivic sheaves' available that admits the standard yoga of the six functors.
Is there ...

A recent paper of Ben-Zvi and Nadler gives a general formalism for understanding "dimensions" in sheaf theories. Without getting too far into details, amongst other things, this formalism allows us ...

Let $X$ be a smooth complex projective variety acted upon algebraically by a complex torus $T$. Suppose that $\{X_{\beta}\}_{\beta\in B}$ is a finite $T$-invariant stratification of $X$ into smooth ...

Let $X$ be a complex variety acted upon algebraically by a complex torus $T$. Suppose that $\{X_{\beta}\}_{\beta\in S}$ is a finite $T$-equivariant stratification of $X$, so that the $X_{\beta}$ are ...

Let $T$ be a real torus, and let $X$ and $Y$ be $T$-spaces. Under what conditions (if any) will the existence of graded $H^*_T$-algebra isomorphism between the $T$-equivariant cohomologies of $X$ and ...

I'm having a surprisingly hard time finding references for some facts about $GL_k$-equivariant cohomology of the space of $k\times n$ matrices. Specifically, I believe the following things to be true:
...

Let $T$ be a complex torus and $X$ a smooth quasi-projective $T$-variety with finitely many fixed points. Denote by $\varphi:H_{T}(X)\rightarrow H_{T}(X^T)$ the map on equivariant cohomology induced ...

Given an action of a group $G$ on a topological space $X$, the associated homotopy quotient is $$X_G := (EG \times X)/G,$$ where $EG$ is the total space of a universal principal $G$-bundle $EG \to BG$ ...

Let $M$ be a (discrete) monoid acting on a space $X.$ We may take the quotient of $X,$ by this action, $X/M$ that is the coequalizer of the action map $M \times X \to X$ against the projection map. ...

We want to calculate $H^{k}_{S^1}(S^2)$. We can choose two open sets $U=S^{2} \setminus p_{+}$ and $V = S^{2} \setminus p_{-}$, where $p_{+}$ and $p_{-}$ are the north and south pole of $S^{2}$. They ...

This is somewhat related to a question that I asked on Math.SE but, sadly, received no response. I apologize ahead of time if this is not appropriate for MO. Feel free to vote to close if this is the ...

After studying some foundation of Gromow-Witten invariants, I now would like to see an explicit computation. I heard that one should first take a look at the total space of $\mathcal{O}(-1)^{\oplus2}$ ...

First let's consider equivariant cohomology: if a compact Lie group $G$ acts on a compact manifold $M$. We have the equivariant cohomology $ H_G(M)$ defined as the cohomology of the cochain complex ...